I find it interesting that you guys call a barrel "cover" as apposed to concealment. I also find it interesting that you train to shoot over your cover/concealment. I was trained never to shoot over top of the cover/concealment, but rather to always shoot around it. The reasoning for it was that by shooting over it, you are exposing your head and giving the bad guy a target to shoot at. By shooting around the cover/concealment you expose a minimal part of your body and its always "gun first" when looking around the corner.
My original instructor demonstrated this by using an orange gun... he had us all line up infront of our targets and he stood behind the barrel. He asked us to tell him when we thought we had enough of a target to fire on him. Before we had anything worth shooting at, he told us how much of our body he could see. He, in most cases, had a diaginal line from our farthest shoulder downward through our center mass ( like right shoulder to left foot).
And as far as kneeling, strong hand+strong knee down. Knee sticking out fromthe side of the barrel would warrant a kick in the leg to let us know we could be shot in the leg.